The effect of grain-size on the stress and velocity fields ahead of a crack in a material which deforms by Coble creep

Abstract

The stress and velocity fields ahead of a grain-boundary crack in a material which deforms by Coble creep are investigated for a series of grain sizes using the numerical analysis technique established by Cocks I-1-3]. The numerical results are compared with the linear viscous fields obtained by the boundary element method and the finite element method. It is demonstrated that a detailed knowledge of the micromechanical processes of material transport and deformation are required to determine the stress and displacement fields for the grains which immediately surround the crack tip. But the response of the surrounding material can be adequately described from a conventional linear viscous analysis of the problem.

Void growth ahead of a dominant crack in a material which deforms by coble creep

“…We should note that in this limit the void growth rate is determined by the in-plane mean stress and contours of constant void growth rate about the crack tip, Fig. 11, have the same shape as contours of constant mean stress [5].…”

“…The stress predicted by a continuum analysis changes significantly over length scales comparable to the facet length in the vicinity of the crack tip, and the scale of the problem considered here is such that higher order terms in the expressions for the stress about the crack tip become important beyond the second grain and by the third grain 0.11 is only half 0"22. Also the micro-stresses are not directly related to the macro-stresses [5]. We can identify two types of boundaries in Fig.…”

“…l(a) is presented in Table 1 in which the stress intensity factor K/(aoxfld) obtained from the Boundary Element Analysis of the continuum problem of Fig. l(b) is also given [5].…”

“…1 are fully described in an accompanying paper [5]. The procedures are based on a variational principle originally proposed by Needleman and Rice [11].…”

“…This computer program has been further extended by the authors to provide a computer package NAD-GB (Numerical Analysis of Diffusion along Grain-Boundaries) which contains powerful pre-and post processors, allowing problems with large numbers of degrees of freedom to be formulated and the results of the analyses to be graphically presented in various styles [10]. The effect of grain structure on the crack tip fields in the absence of any voids has been addressed in an accompanying paper [5]. In the present paper, void growth within a body which contains a dominant crack is investigated.…”